Ted Thorndike is trying to close a sale with the Alvindale Chipmunks, a minor-league professional baseball team. Although his grandfather isn't very thrilled about any kind of deal with somebody with a name like "Chipmunks," Ted feels this could mark the beginning of some really high-level business with professional baseball teams, all the way up to the majors.

The Chipmunks, who are relatively high tech for a minor-league team, have been using a Thorndike competitor's auto matic pitching machine for batting prac tice and are looking for a replacement. The problem is that the machine is very erratic. Although it has not "beaned" any players yet, they are concerned about the amount of vertical variability it exhibits in its pitches. Tom Johnson, principal owner of the Chipmunks, did a study in which he set up a target at home plate, then measured the heights at which the balls hit the target.

Mr. Johnson found the heights were normally distributed, as he has discovered is the case for pitching machines throughout the industry. However, he feels that a standard deviation of 3.5 inches in the heights of the pitches is just too "wild," even for the minor-league level. He has offered Ted Thorndike the opportunity to supply a replacement machine. The only catch to the sale is that Ted must prove that the Thorndike "Rapid Robot" machine is significantly better than the machine the Chipmunks are now using. Mr. Johnson has specified that the Thorndike pitcher will be purchased only if it passes the following test: Based on 30 pitches by Rapid Robot, the standard deviation of the vertical heights must be significantly less than 3.5 inches, and at the 0.01 level of significance.

All of this talk about vertical standard deviation is over Luke's head, but he tells Ted to go ahead and see if he can swing a deal with the Chipmunks. Ted is confident that the Thorndike Rapid Robot can meet Mr. Johnson's specifications, so he and Mr. Robot make the trip to Alvindale.

Ted and Mr. Johnson set up the Thorndike Rapid Robot machine at the team's practice facility, along with a target at home plate that will reveal exactly where each pitch lands. Measured from ground level at home plate, the 30 pitches are the following distances from the ground. The data are also in file THORN13.

1. Given Mr. Johnson's decision rule, is this a two-tail or a one-tail hypothesis test? What are the null and alternative hypotheses?

2. When Mr. Johnson has completed his analysis of the data represented by the pitches in the test session, will he sign Thorndike's Rapid Robot as a mechanical member of the Chipmunks?

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